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Dispersivity variations of solute transport in heterogeneous sediments: numerical and experimental study

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Abstract

Heterogeneity significantly effects the accuracy of flow and contaminant transport prediction in subsurface formations. The spatial correlation structure of hydraulic conductivity (K) is a crucial factor to characterize the heterogeneous architecture. In presented study, the relationship between the spatial correlation structure of K and plume dispersion is analyzed through the integration of experimental and numerical simulation approaches. A detailed description on the sedimentary facies types in a column experiment is obtained to ensure the accuracy of the heterogeneous characterization. The spatial correlation structure of K is analyzed with the components of ln(K) covariance and facies transition probability structures. Lagrangian-based models are developed to estimate solute dispersion in nonreactive tracer injection experiments. The results show that the model can predict plume spreading accurately when the spatial correlation structure is well defined. The dispersivities calculated by the Lagrangian-based model are slightly higher than those obtained from the solute transport experiments. Further, the upscaled dispersivity derived from the transition probability is dominated by the cross-transition probability structure, while the contribution of the auto-transition terms is quite small. The numerical modeling results confirm that the upscaled dispersivity can reproduce the solute breakthrough in the heterogeneous sediment well. The scale dependence of dispersion is strengthened when the flow direction is perpendicular to the bedding plane where the conductivity dramatically changes along the flow path in a layered bedding sediment.

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Availability of data and material

The data and material used to support the findings of this study are available from the corresponding author upon request.

Abbreviations

\({\alpha }_{11}^{l}\) :

Longitudinal dispersivity

\({\alpha }_{22}^{l}\) :

Transverse dispersivity

\({\alpha }_{33}^{l}\) :

Lateral dispersivity

\({\alpha }_{11}^{e}\) :

Effective longitudinal dispersivities

\({\alpha }_{11}^{ul}\) :

Upscaled longitudinal dispersivity

C :

Concentration

C 0 :

Initial concentration

C ii(h ϕ):

Auto-covariance in direction ϕ

C ij(h ϕ):

Cross-covariance in direction ϕ

C Y(h ϕ):

Global covariance

D :

Hydrodynamic dispersion coefficient

erfc :

Complementary error function

g :

Mean hydraulic gradient

i, j :

Facies type

I i(x):

Indicator space function

J 0 :

Zero-order Bessel function

J 1 :

First-order Bessel function

K :

Hydraulic conductivity

m i :

Mean

M Y :

Global mean

n :

Porosity

p i :

Volume proportion

R :

Retardation factor

x :

Spatial coordinate

t :

Time

t ij(h ϕ):

Transition probability in direction ϕ

U 1 :

Mean velocity

v :

Pore velocity

Y(x):

Global log conductivity

Y i(x):

Log conductivity

Z :

Integral variable

σ i 2 :

Variance

σ Y 2 :

Global variance

δ ij :

Kronecker delta

λ i :

Integral scale

λ I :

Indicator correlation scale

λ hi :

Horizontal integral scale

λ vi :

Vertical integral scale

λ Y :

Global integral scale

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Acknowledgements

This work was jointly supported by the National Key Research and Development Program of China (No. 2018YFC1800900), the Program for Jilin University (JLU) Science and Technology Innovative Research Team (No. 2019TD-35), the National Natural Science Foundation of China (No: 41772253, 41972249) and the Graduate Innovation Fund of Jilin University (101832020CX233). Additional funding was provided by the Engineering Research Center of Geothermal Resources Development Technology and Equipment, Ministry of Education, China.

Funding

This work was jointly supported by the National Key Research and Development Program of China (No. 2018YFC1800900), the National Natural Science Foundation of China (No: 41772253, 41972249), the Program for Jilin University (JLU) Science and Technology Innovative Research Team (No. 2019TD-35) and the Graduate Innovation Fund of Jilin University (101832020CX233). Additional funding was provided by the Engineering Research Center of Geothermal Resources Development Technology and Equipment, Ministry of Education, China.

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Authors and Affiliations

  1. College of Construction Engineering, Jilin University, Changchun, 130026, P. R. China

    Ziqi Ma, Zhenxue Dai, Xiaoying Zhang & Chuanjun Zhan

  2. Engineering Research Center of Geothermal Resources Development Technology and Equipment, Ministry of Education, Jilin University, Changchun, 130026, P. R. China

    Zhenxue Dai

  3. College of Resource Environment and Tourism, Laboratory Cultivation Base of Environment Process and Digital Simulation, Laboratory of Water Resources Security, Capital Normal University, Beijing, 100048, P. R. China

    Huili Gong & Lin Zhu

  4. Department of Geology, University of Cincinnati, Cincinnati, OH, 45220, USA

    Corey D. Wallace & Mohamad Reza Soltanian

  5. Department of Environmental Engineering, University of Cincinnati, Cincinnati, OH, 45220, USA

    Mohamad Reza Soltanian

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  1. Ziqi Ma
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  2. Zhenxue Dai
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  3. Xiaoying Zhang
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  5. Huili Gong
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  6. Lin Zhu
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  7. Corey D. Wallace
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  8. Mohamad Reza Soltanian
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Contributions

Conceptualization: Ziqi Ma, Zhenxue Dai; Methodology: Ziqi Ma, Zhenxue Dai, Xiaoying Zhang; Formal analysis and investigation: Ziqi Ma, Chuanjun Zhan, Lin Zhu; Writing—original draft preparation: Ziqi Ma, Chuanjun Zhan; Writing – review and editing: Zhenxue Dai, Huili Gong, Corey Wallace, Mohamad Reza Soltanian; Funding acquisition: Zhenxue Dai, Xiaoying Zhang; Supervision: Zhenxue Dai.

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Correspondence to Xiaoying Zhang or Chuanjun Zhan.

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Appendix

Appendix

Table 4 Layer thicknesses in the heterogeneous soil column
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Ma, Z., Dai, Z., Zhang, X. et al. Dispersivity variations of solute transport in heterogeneous sediments: numerical and experimental study. Stoch Environ Res Risk Assess 36, 661–677 (2022). https://doi.org/10.1007/s00477-021-02040-x

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